5. Consider the second-order linear homogeneous recurrence relation ak = ak-1 + 6 ak-2.
To find a sequence which satisfies this recurrence relation and also satisfies the initial conditions, you need to start by finding the two sequences which satisfy the relation by solving the characteristic equation. The characteristic equation of the relation is t2 - t - 6 = 0.
You might like to refer back to Example 8.3.3 on pages 457 and 458 of your textbook.